According to H&R Block, "A dependent is a full-time student if the dependent is enrolled in a school for the number of hours or courses considered by the school to be full-time during some part of at least 5 calendar months during the year..." 12 credit hours or more is generally considered full-time, and the age limit on this is 24.

No, because homeschools can still legally count as private schools. Some states may be a bit ambiguous on this, but for those you can sign up under an umbrella school. As for the credit hours, just do work equivalent to that number of credit hours.